As geometries continue to shrink, manufacturers of semiconductor devices need continually to improve the control of their manufacturing processes. At the same time as layer thicknesses and feature sizes decrease, so also the complexity of the structures to be measured and of the materials within those structures increases. In many cases it becomes necessary to characterize material properties that were previously neglected to the first order, or to find new methods of characterization where the limitations of previous methods have become significant obstacles to progress.
For a long time, optical techniques have been favored for measuring the thicknesses and other properties of transparent or semi-transparent films. Techniques of this type, known generally as optical metrology, operate by illuminating a sample with electromagnetic radiation (typically referred to as a probe beam) and then detecting and analyzing the reflected energy. They have the advantage of being non-contact and non-destructive, and they can provide high throughput and almost arbitrarily small measurement spot sizes (ultimately limited only by the wavelength of the probe beam).
Two broad classes of optical technique commonly used in this context are Reflectometry and Ellipsometry. In Reflectometry, changes in the amplitude of the reflected light are measured, usually as a function of either the angle of incidence or the wavelength of the probe beam. The latter case is more usually referred to as Spectrophotometry, or just Spectrometry. In Ellipsometry, the change in polarization of the probe beam is measured, usually by quantifying the difference in sample reflectance between s-polarized light (in which the electric field vector is perpendicular to the plane of incidence) and p-polarized (in which it is parallel to the plane). This too can be carried out as a function of either the angle of incidence or the wavelength of the light.
A variety of such techniques can be combined on a common platform, as is the case with the Opti-Probe® tool offered by the Assignee and conceptually described in U.S. Pat. No. 5,798,837 which is incorporated in this document by reference. In particular, this tool combines a proprietary method of single-wavelength Reflectometry, a method of Spectrophotometry and three complementary methods of Ellipsometry which can be employed singly or in any combination.
In addition to film thickness, techniques of this type may be used to analyze a wide range of attributes including refractive index and extinction, crystallinity, composition, porosity and roughness. To measure the doping level in a semiconductor material, however, it has often been necessary to resort to a non-optical technique such as Secondary Ion Mass Spectrometry (SIMS) or resistivity modeling.
An optical technique does not of course measure the material attributes directly, but by comparing the reflected light from the sample with the calculated reflectance of a “model filmstack”. The computer program controlling this process is customarily referred to as a “recipe”, and the aim of the recipe is to find the model that is the most faithful possible representation of the sample. This is done by regressively optimizing the parameters that describe the model filmstack until there is the closest possible correspondence between the calculated reflectance of the model and the actual reflectance of the sample. The outputs from the recipe are the parameters describing the model filmstack. It is customary to quantify the closeness of the correspondence between the calculated and actual reflectances by means of a “Residual” or “Goodness of Fit” (GOF) parameter.
It can therefore be seen that the success of such an approach depends upon being able to choose parameters that accurately represent the physical attributes of the sample. For any film layer, these parameters include thickness as well as dielectric properties of the material. Typically, these parameters are expressed in terms of the sample's optical dispersion; that is, the manner in which the complex refractive index (N=n−ik) or complex dielectric function (∈=∈1+i∈2) varies as a function of the wavelength or (equivalently) photon energy of the light. There is a large class of models that enable these functions to be represented parametrically. Simplest of all is the lookup-table approach, in which case the values of n and k (or ∈1 and ∈2) at each wavelength are effectively independent parameters, but it is usual to seek to reduce the number of parameters using a mathematical formula of some sort. The most familiar is the Cauchy model, whereby n and k are represented as an expansion of the form
                                          n            ⁡                          (              λ              )                                =                                    n              0                        +                                          n                1                                            λ                2                                      +                                          n                2                                            λ                4                                      +            ⋯                          ⁢                                  ⁢                              k            ⁡                          (              λ              )                                =                                    k              0                        +                                          k                1                                            λ                2                                      +                                          k                2                                            λ                4                                      +            ⋯                                              (        1        )            
However, this still suffers from the drawback that n and k are regarded as being independent functions, whereas in fact they are not: they are related via the Kramers-Kronig transform, viz.
                              n          +          ik                =                                            ɛ              1                        +                          i              ⁢                                                          ⁢                              ɛ                2                                                                        (        2        )            
                                          ɛ            1                    ⁡                      (                          E              0                        )                          =                  1          +                                    ∫              0              ∞                        ⁢                                                            E                  ⁢                                                                          ⁢                                                            ɛ                      2                                        ⁡                                          (                      E                      )                                                                                                            E                    2                                    -                                      E                    0                    2                                                              ⁢                                                          ⁢                              ⅆ                E                                                                        (        3        )            
By far the most satisfactory models are those that explicitly satisfy this condition, but even of these there are a great many. Most involve the use of ensembles of oscillators, either of classical Lorentz form (see, for example, C. Ygartua and M. Liaw, “Characterization of epitaxial silicon germanium thin films by spectroscopic ellipsometry”, Thin Solid Films 313–314, 237 (1998)) or of modified harmonic form (see, for example, J. Leng, J. Opsal, H. Chu, M. Senko and D. E. Aspnes, “Analytical representations of the dielectric functions of materials for device and structural modeling”, Thin Solid films 313–314, 132 (1998), C. C. Kim, J. W. Garland, H. Abad and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation”, Phys. Rev. B45, 11749 (1992), or F. L. Terry, “A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGal-xAs”, J. Appl. Phys. 70, 409 (1991)). Models also exist to combine two or more pre-existing Kramers-Kronig consistent dispersions into a resultant dispersion, either via an effective-medium approximation (EMA—see, for example, M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso and D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation”, J. Appl. Phys. 56, 2664 (1984) which, incidentally, also presents an early version of the harmonic oscillator model) or an Alloy model (see, for example, D. E. Aspnes, S. M. Kelso, R. A. Logan and R. Bhat, “Optical properties of AlxGal-xAs”, J. Appl. Phys. 60, 754 (1986) and P. G. Snyder, J. A. Woollam, S. A. Alterovitz and B. Johs, “Modeling AlxGal-xAs optical constants as functions of composition”, J. Appl. Phys. 68, 5925 (1990)).
However, none of these techniques are naturally suited to modeling the specific effects that doping has upon the dielectric functions of semiconductors. The presence of dopants can have a significant effect on the dielectric response of semiconductor materials. To illustrate, FIG. 1 shows measured values for ∈2 plotted as a function of photon energies for Silicon. As shown, the ∈2 curve has two strong features. These occur at photon energies of ˜3.4 eV and 4.2 eV and are denoted “E1” and “E2” respectively. As described in “Effects of Heavy Doping on the Optical Properties and the Band Structure of Silicon” (L. Viña and M. Cardona, Phys. Rev. B29, 6739 (1984), and contemporaneously by D. E. Aspnes, A. A. Studna and E. Kinsbron in “Dielectric properties of heavily doped crystalline and amorphous silicon from 1.5 to 6.0 eV”, Phys. Rev. B29, 768 (1984)) the principal effect of doping on the optical properties of these materials is to suppress, and at higher doping levels shift, the E1 and E2 features (with the effect on the E1 feature typically being more profound). This is verified by modeling the dielectric function of a doped epitaxial Si film (with a Boron content of ˜2.5×1019 cm−3) on a nominally undoped Si substrate, as also shown in FIG. 1. The limitations of the existing models are these: firstly, in the oscillator methods each feature in the ∈2 curve is made up of contributions from more than one oscillator, so it is difficult to correlate subtle changes in the shapes of features with specific oscillator parameters. Secondly, because of this “nonlocal” nature of oscillator models, the ability to fit the shape of a feature in one part of the spectrum where data is available may be hindered by the unavailability of data from another part of the spectrum. A practical example of this is when a SiGe layer buried under an epitaxial Si cap must be measured, as the Si cap is opaque to wavelengths of light in the DUV region (photon energies above ˜3 eV) and so no information about the SiGe is available in this range (which includes the positions of both the E1 and E2 peaks). The method of Herzinger et al., in U.S. Pat. No. 5,796,983, would seem to address the first of these limitations but not the second. Alloy or EMA models could be used to interpolate between different dispersion curves corresponding to known levels of doping, but this could only work if all other material properties (e.g. Germanium content in a SiGe film) could be assumed constant. Moreover, the component models with known doping levels would need to exist for the particular combination of other material properties being studied, and this would not generally be the case.
Other effects that can cause similar subtle changes to the dielectric functions of the film are strain (see for example U. Schmid, J. Humlí{hacek over (c)}ek, F. Luke{hacek over (s)}, M. Cardona, H. Presting, H. Kibbel, E. Kasper, K. Eberl, W. Wegscheider and G. Abstreiter, “Optical transitions in strained Ge/Si superlattices”, Phys. Rev. B45, 6793 (1992)) and (in very thin films, of the order of tens of nanometers or less) quantum confinement (see, for example, D. V. Lang, R. People, J. C. Bean and A. M. Sergent, “Measurement of the band gap of GexSi1-x/Si strained-layer heterostructures”, Appl. Phys. Lett. 47, 1333 (1985)).
There is therefore a need for a technique that can decouple these subtle effects from the complex overall structure of the semiconductor's dielectric functions. Such a technique should be able to distinguish changes in, for example, doping level from other things that may affect the material's optical properties (such as changing Ge content in a SiGe film), extract such information even when optical data is only available from a limited wavelength range (such as, for example, a doped SiGe layer buried under an epitaxial Si cap), and enable an efficient computational algorithm to implement the technique in the context of real-time production measurement. The present invention provides such a technique.